Covariant gauge-natural conservation laws

TL;DR

This paper explores the conditions under which gauge-natural lifts generate covariant conservation laws, emphasizing the role of generalized Jacobi equations in identifying canonical generators of physical charges.

Contribution

It establishes a criterion based on generalized Jacobi equations for selecting gauge-natural lifts that produce canonical covariant conservation laws.

Findings

Vertical parts of gauge-natural lifts in the kernel of Jacobi morphisms generate covariant currents.

Only specific gauge-natural lifts serve as canonical generators of physical charges.

The framework links variational principles with conservation laws in gauge-natural theories.

Abstract

When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equations for the gauge-natural invariant Lagrangian. {\em Vice versa} all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms which are in the kernel of generalized Jacobi morphisms are generators of canonical covariant currents and superpotentials. In particular, only a few gauge-natural lifts can be considered as {\em canonical} generators of covariant gauge-natural physical charges.